Bootstrap Confidence Sets for Spectral Projectors of Sample Covariance

A. Naumov, V. Spokoiny and V. Ulyanovk

No 2018-024, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: Let X1, . . . ,Xn be i.i.d. sample in Rp with zero mean and the covariance matrix . The problem of recovering the projector onto an eigenspace of from these observations naturally arises in many applications. Recent technique from [9] helps to study the asymp- totic distribution of the distance in the Frobenius norm kPr - bP rk2 between the true projector Pr on the subspace of the rth eigenvalue and its empirical counterpart bP r in terms of the effective rank of . This paper offers a bootstrap procedure for building sharp confidence sets for the true projector Pr from the given data. This procedure does not rely on the asymptotic distribution of kPr - bP rk2 and its moments. It could be applied for small or moderate sample size n and large dimension p. The main result states the validity of the proposed procedure for finite samples with an explicit error bound for the er- ror of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high-dimensional spaces. Numeric results confirm a good performance of the method in realistic examples.

JEL-codes: C00 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

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